Torn Shapes

Stage: 2 Challenge Level:

Another well answered problem!
Particularly clear solutions were sent in by James from St Mary's
School, Sara-Louise from Perton Middle School and Rowena from
Christ Church Infants. Sara-Louise said:

My method for this problem was to count the number of squares along
one side, then times them by the number of squares along the other
side.
For the rectangles that were made up of two shapes, I first split
the single shape into two, timesed the number of squares along the
sides of the shapes (separately), then added them together.

Rowena had a slightly different way of finding
out the number of squares taken up by each shape. She wrote:

I am going to count the whole squares up and across, then draw the
outline of the rectangle, and then draw the squares on to it that
weren't there before. I will count the squares and put the total
into a table.

Here's Rowena's table:

Rectangle

Number of Squares

Orange

3 down x 5 across = 15

Blue

4 down x 8 across = 32

Green

5 down x 3 across = 15

Yellow

5 down by 6 across = 30

Pale orange

21

Purple

18

For the final shape, James said:

There were $3$ in the column for the last puzzle and I could
see a bit of a sixth square so the smallest number was $3 \times 6
= 18$. The longest shape had $8$ in a row so the most it could have
is $3 \times 8 = 24$.

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